Mean values of local operators in highly excited Bethe states

Pozsgay, Balázs

doi:10.1088/1742-5468/2011/01/p01011

Cited by 99 publications

(182 citation statements)

References 62 publications

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“…. M ; (iv) the residues of the form factors are given by the following recursive relations Note that the recursive relation (42), first derived in [55], was also discussed in the recent papers [48,49,52]. In particular, in [48,49] its connection with recursive relations appearing in integrable quantum field theory were investigated.…”

Section: Properties Of the Form Factors And Proof Of The Determinant mentioning

confidence: 98%

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Exact formulas for the form factors of local operators in the Lieb–Liniger model

Piroli¹,

Calabrese²

2015

J. Phys. A: Math. Theor.

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Abstract. We present exact formulas for the form factors of local operators in the repulsive Lieb-Liniger model at finite size. These are essential ingredients for both numerical and analytical calculations. From the theory of Algebraic Bethe Ansatz, it is known that the form factors of local operators satisfy a particular type of recursive relations. We show that in some cases these relations can be used directly to derive practical expressions in terms of the determinant of a matrix whose dimension scales linearly with the system size. Our main results are determinant formulas for the form factors of the operators (Ψ † (0)) 2 Ψ 2 (0) and Ψ R (0), for arbitrary integer R, where Ψ, Ψ † are the usual field operators. From these expressions, we also derive the infinite size limit of the form factors of these local operators in the attractive regime.

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Section: Properties Of the Form Factors And Proof Of The Determinant mentioning

confidence: 98%

“…It is given by the following proposition regarding some fundamental properties of the form factors of local operators [5,25,48,49,55,52].…”

Section: Properties Of the Form Factors And Proof Of The Determinant mentioning

confidence: 99%

Exact formulas for the form factors of local operators in the Lieb–Liniger model

Piroli¹,

Calabrese²

2015

J. Phys. A: Math. Theor.

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“…The corresponding right eigenvector |1; R is independent of x, η, and A (±) and can be determined explicitly. If the matrices A (±) satisfy (2.13) it has the form 18) where the vectors {|a 1 , . .…”

Section: A Generating Function For Translationally Invariant Matrix-mentioning

confidence: 99%

“…For integrable models, the existence of local conservation laws strongly constrains the dynamics, and it has been proposed 7 that stationary values are described by a generalised Gibbs ensemble (GGE). By now rather convincing evidence supporting this proposal has accumulated [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] , but a general proof is still outstanding. Whereas in equilibrium integrability may be viewed chiefly as powerful tool for obtaining exact solutions of paradigmatic models, out of equilibrium it is an essential physical feature.…”

Section: Introductionmentioning

confidence: 99%

Relaxation after quantum quenches in the spin-12Heisenberg XXZ chain

et al. 2014

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We consider the time evolution after quantum quenches in the spin-1/2 Heisenberg XXZ quantum spin chain with Ising-like anisotropy. The time evolution of short-distance spin-spin correlation functions is studied by numerical tensor network techniques for a variety of initial states, including Néel and Majumdar-Ghosh states and the ground state of the XXZ chain at large values of the anisotropy. The various correlators appear to approach stationary values, which are found to be in good agreement with the results of exact calculations of stationary expectation values in appropriate generalized Gibbs ensembles. In particular, our analysis shows how symmetries of the post-quench Hamiltonian that are broken by particular initial states are restored at late times.

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“…This is characterized by appropriate particle/hole distribution functions ρ p,h j (x) for of elementary excitations labelled by the index j (x parametrizes the respective momenta). The corresponding "microcanonical" description [42,52,53] is based on the particular simultaneous eigenstate |Φ s of the Hamiltonian and the higher conservation laws, characterized by the set {ρ p,h j (x)} in the thermodynamic limit. One then considers small changes of this microstate, and determines the resulting O(1) (i.e.…”

mentioning

confidence: 99%

“Light-Cone” Dynamics After Quantum Quenches in Spin Chains

2014

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Signal propagation in the non equilibirum evolution after quantum quenches has recently attracted much experimental and theoretical interest. A key question arising in this context is what principles, and which of the properties of the quench, determine the characteristic propagation velocity. Here we investigate such issues for a class of quench protocols in one of the central paradigms of interacting many-particle quantum systems, the spin-1/2 Heisenberg XXZ chain. We consider quenches from a variety of initial thermal density matrices to the same final Hamiltonian using matrix product state methods. The spreading velocities are observed to vary substantially with the initial density matrix. However, we achieve a striking data collapse when the spreading velocity is considered to be a function of the excess energy. Using the fact that the XXZ chain is integrable, we present an explanation of the observed velocities in terms of "excitations" in an appropriately defined generalized Gibbs ensemble.The last few years have witnessed a number of significant advances in understanding the nonequilibirum dynamics in isolated quantum systems. Much of this activity has focussed on fundamental concepts such as thermalization [1][2][3][4][5] or the roles played by dimensionality and conservation laws [6][7][8][9][10][11][12][13][14][15][16].Another key issue concerns the spreading of correlations out of equilibrium, and in particular the "light-cone" effect after global quantum quenches. The most commonly studied protocol in this context is to prepare the system in the ground state of a given Hamiltonian, and to then suddenly change a system parameter such as a magnetic field or interaction strength. At subsequent times the spreading of correlations can then be analyzed by considering the time-dependence of two-point functions of local operators separated by a fixed distance. As shown by Lieb and Robinson [17,18], the velocity of information transfer in quantum systems is bounded. This gives rise to a causal structure in commutators of local operators at different times, although Schrödinger's equation, unlike relativistic theories, has no built-in speed limit. Recently, the Lieb-Robinson bounds have been refined [19][20][21] and extended to mixed state dynamics in open quantum systems [21,22] as well as creation of topological quantum order [23].A striking consequence of the Lieb-Robinson bound is that the equal-time correlators after a quantum quench feature a "light-cone" effect [23], which is most pronounced for quenches to conformal field theories from initial density matrices with a finite correlation length [24]: connected correlations are initially absent, but exhibit a marked increase after a time t 0 = x/2v. This observation is explained by noting [25,26] that entangled pairs of quasi-particles initially located half-way between the two points of measurement, propagate with the speed of light v and hence induce correlations after a time t 0 . These predictions have been verified numerically in several systems, se...

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Mean values of local operators in highly excited Bethe states

Cited by 99 publications

References 62 publications

Exact formulas for the form factors of local operators in the Lieb–Liniger model

Exact formulas for the form factors of local operators in the Lieb–Liniger model

Relaxation after quantum quenches in the spin-12Heisenberg XXZ chain

“Light-Cone” Dynamics After Quantum Quenches in Spin Chains

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